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A192256 0-sequence of reduction of (n^3) by x^2 -> x+1. 2
1, 1, 28, 92, 342, 990, 2705, 6801, 16278, 37278, 82532, 177572, 373105, 768241, 1554616, 3098808, 6095738, 11851922, 22805745, 43477745, 82197986, 154231706, 287411688, 532248552, 980014177, 1794978145, 3271695220, 5936514356, 10726952958 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".

LINKS

Table of n, a(n) for n=1..29.

FORMULA

Empirical G.f.: x*(1-4*x+29*x^2-36*x^3+43*x^4-16*x^5+2*x^6)/(1-x)/(1-x-x^2)^4. [Colin Barker, Feb 10 2012]

MATHEMATICA

c[n_] := n^3;  (* A000578 *)

Table[c[n], {n, 1, 15}]

q[x_] := x + 1;

p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]

reductionRules = {x^y_?EvenQ -> q[x]^(y/2),

   x^y_?OddQ -> x q[x]^((y - 1)/2)};

t = Table[

  Last[Most[

    FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,

   30}]

Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192256 *)

Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192257 *)

(* by Peter J. C. Moses, Jun 20 2011 *)

CROSSREFS

Cf. A192232, A192257.

Sequence in context: A044596 A331765 A333280 * A005971 A189808 A130085

Adjacent sequences:  A192253 A192254 A192255 * A192257 A192258 A192259

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 27 2011

STATUS

approved

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Last modified April 9 12:51 EDT 2020. Contains 333352 sequences. (Running on oeis4.)